Charging car battery with another car - circuit schematic

Question

I came across an example in a textbook that talked about charging a dead car battery with another car battery. They provided this picture of how to connect the two batteries: -

Source: Engineering Circuit Analysis - 12th edition - page 6 - Irwin

They correctly note that because the current flows from + to - in the "Weak battery" it charges, while the "Good battery" discharges, because the current flows from - to +.

Let's assume the "Good battery" is 12 V and the "Weak battery" is 9 V. Then, the associated circuit diagram must look like this: -

^{simulate this circuit – Schematic created using CircuitLab}

The diagram contains a contradiction, because the voltage drop cannot be both 12 V and 9 V. But in real life, it is indeed possible to charge a dead car battery like this. What is missing from the circuit diagram for this to not contradict itself?

Answer 1

Internal resistance

The batteries are not ideal voltage sources, far from it. The first order simulation has to add the internal resistance, which varies with age, temperature, discharge etc, but it will look something like this:

^{simulate this circuit – Schematic created using CircuitLab}

That's why, when you measure a bad battery, it may still read a pretty high voltage but will drop to half when loaded.